This article reviews the range of Markov models and their extensions that can be fitted to panel data using the R package `msm`. Panel data are observations of a continuous-time process at arbitrary times, such as visits to a hospital to diagnose disease status. The article covers the implementation of these models in the `msm` package, which is designed to be straightforward to use, flexible, and comprehensively documented. Key topics include: 1. **Markov Multi-State Models**: Definitions, assumptions, and likelihood calculations for panel data. 2. **The msm Package**: Overview, features, and examples of its use. 3. **Model Specification and Estimation**: How to specify and estimate Markov models, including handling covariates and time-inhomogeneity. 4. **Hidden Markov Models**: Fitting hidden Markov models to panel data, including misclassification models. 5. **Model Assessment**: Diagnostic plots, formal goodness-of-fit tests, and other issues in model assessment. The article provides detailed examples using real-world data, such as monitoring heart transplant recipients and lung transplant recipients, to illustrate the application of multi-state models and the use of the `msm` package. It also discusses the handling of censored states and the estimation of transition probabilities over time intervals.This article reviews the range of Markov models and their extensions that can be fitted to panel data using the R package `msm`. Panel data are observations of a continuous-time process at arbitrary times, such as visits to a hospital to diagnose disease status. The article covers the implementation of these models in the `msm` package, which is designed to be straightforward to use, flexible, and comprehensively documented. Key topics include: 1. **Markov Multi-State Models**: Definitions, assumptions, and likelihood calculations for panel data. 2. **The msm Package**: Overview, features, and examples of its use. 3. **Model Specification and Estimation**: How to specify and estimate Markov models, including handling covariates and time-inhomogeneity. 4. **Hidden Markov Models**: Fitting hidden Markov models to panel data, including misclassification models. 5. **Model Assessment**: Diagnostic plots, formal goodness-of-fit tests, and other issues in model assessment. The article provides detailed examples using real-world data, such as monitoring heart transplant recipients and lung transplant recipients, to illustrate the application of multi-state models and the use of the `msm` package. It also discusses the handling of censored states and the estimation of transition probabilities over time intervals.